Notes on Low-rank Matrix Factorization

Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing an original matrix to low-rank matrices, MF provides a unified method for dimension reduction, clustering, and matrix completion. In this article we review several important variants of MF, including: Basic MF, Non-negative MF, Orthogonal non-negative MF. As can be told from their names, non-negative MF and orthogonal non-negative MF are variants of basic MF with non-negativity and/or orthogonality constraints. Such constraints are useful in specific senarios. In the first part of this article, we introduce, for each of these models, the application scenarios, the distinctive properties, and the optimizing method. By properly adapting MF, we can go beyond the problem of clustering and matrix completion. In the second part of this article, we will extend MF to sparse matrix compeletion, enhance matrix compeletion using various regularization methods, and make use of MF for (semi-)supervised learning by introducing latent space reinforcement and transformation. We will see that MF is not only a useful model but also as a flexible framework that is applicable for various prediction problems

Analytic Campanato Spaces and Their Compositions

This paper is devoted to characterizing the analytic Campanato spaces $\mathcal{AL}_{p,\eta}$ (including the analytic Morrey spaces, the analytic John-Nirenberg space, and the analytic Lipschitz/H\"older spaces) on the complex unit disk $\mathbb D$ in terms of the M\"obius mapping and the Littlewood-Paley form, and consequently their compositions with the analytic self-maps of $\mathbb D$.Comment: 23 page

Are residues in a protein folding nucleus evolutionarily conserved?

It is important to understand how protein folding and evolution influences each other. Several studies based on entropy calculation correlating experimental measurement of residue participation in folding nucleus and sequence conservation have reached different conclusions. Here we report analysis of conservation of folding nucleus using an evolutionary model alternative to entropy based approaches. We employ a continuous time Markov model of codon substitution to distinguish mutation fixed by evolution and mutation fixed by chance. This model takes into account bias in codon frequency, bias favoring transition over transversion, as well as explicit phylogenetic information. We measure selection pressure using the ratio $\omega$ of synonymous vs. non-synonymous substitution at individual residue site. The $\omega$-values are estimated using the {\sc Paml} method, a maximum-likelihood estimator. Our results show that there is little correlation between the extent of kinetic participation in protein folding nucleus as measured by experimental $\phi$-value and selection pressure as measured by $\omega$-value. In addition, two randomization tests failed to show that folding nucleus residues are significantly more conserved than the whole protein. These results suggest that at the level of codon substitution, there is no indication that folding nucleus residues are significantly more conserved than other residues. We further reconstruct candidate ancestral residues of the folding nucleus and suggest possible test tube mutation studies of ancient folding nucleus.Comment: 15 pages, 4 figures, and 1 table. Accepted by J. Mol. Bio

The ΩDE−ΩM\Omega_{DE}-\Omega_{M} Plane in Dark Energy Cosmology

The dark energy cosmology with the equation of state $w=constant$ is considered in this paper. The $\Omega_{DE}-\Omega_{M}$ plane has been used to study the present state and expansion history of the universe. Through the mathematical analysis, we give the theoretical constraint of cosmological parameters. Together with some observations such as the transition redshift from deceleration to acceleration, more precise constraint on cosmological parameters can be acquired.Comment: 15 pages including 7 figures. Accepted for publication in Modern Physics Letters A (MPLA

Nonlinear dynamical systems and bistability in linearly forced isotropic turbulence

In this letter, we present an extensive study of the linearly forced isotropic turbulence. By using analytical method, we identify two parametric choices, of which they seem to be new as far as our knowledge goes. We prove that the underlying nonlinear dynamical system for linearly forced isotropic turbulence is the general case of a cubic Lienard equation with linear damping. We also discuss a Fokker-Planck approach to this new dynamical system,which is bistable and exhibits two asymmetric and asymptotically stable stationary probability densities.Comment: 7 pages, 1 figur

Online Red Packets: A Large-scale Empirical Study of Gift Giving on WeChat

Gift giving is a ubiquitous social phenomenon, and red packets have been used as monetary gifts in Asian countries for thousands of years. In recent years, online red packets have become widespread in China through the WeChat platform. Exploiting a unique dataset consisting of 61 million group red packets and seven million users, we conduct a large-scale, data-driven study to understand the spread of red packets and the effect of red packets on group activity. We find that the cash flows between provinces are largely consistent with provincial GDP rankings, e.g., red packets are sent from users in the south to those in the north. By distinguishing spontaneous from reciprocal red packets, we reveal the behavioral patterns in sending red packets: males, seniors, and people with more in-group friends are more inclined to spontaneously send red packets, while red packets from females, youths, and people with less in-group friends are more reciprocal. Furthermore, we use propensity score matching to study the external effects of red packets on group dynamics. We show that red packets increase group participation and strengthen in-group relationships, which partly explain the benefits and motivations for sending red packets.Comment: 20 pages, 7 figure

Exploiting Interference for Secrecy Wireless Information and Power Transfer

Radio-frequency (RF) signals enabled wireless information and power transfer (WIPT) is a cost-effective technique to achieve two-way communications and at the same time provide energy supplies for low-power wireless devices. However, the information transmission in WIPT is vulnerable to the eavesdropping by the energy receivers (ERs). To achieve secrecy communications with information nodes (INs) while satisfying the energy transfer requirement of ERs, an efficient solution is to exploit a dual use of the energy signals also as useful interference or artificial noise (AN) to interfere with the ERs, thus preventing against their potential information eavesdropping. Towards this end, this article provides an overview on the joint design of energy and information signals to achieve energy-efficient and secure WIPT under various practical setups, including simultaneous wireless information and power transfer (SWIPT), wireless powered cooperative relaying and jamming, and wireless powered communication networks (WPCN). We also present some research directions that are worth pursuing in the future.Comment: Submitted for possible publicatio

Learning Fixation Point Strategy for Object Detection and Classification

We propose a novel recurrent attentional structure to localize and recognize objects jointly. The network can learn to extract a sequence of local observations with detailed appearance and rough context, instead of sliding windows or convolutions on the entire image. Meanwhile, those observations are fused to complete detection and classification tasks. On training, we present a hybrid loss function to learn the parameters of the multi-task network end-to-end. Particularly, the combination of stochastic and object-awareness strategy, named SA, can select more abundant context and ensure the last fixation close to the object. In addition, we build a real-world dataset to verify the capacity of our method in detecting the object of interest including those small ones. Our method can predict a precise bounding box on an image, and achieve high speed on large images without pooling operations. Experimental results indicate that the proposed method can mine effective context by several local observations. Moreover, the precision and speed are easily improved by changing the number of recurrent steps. Finally, we will open the source code of our proposed approach

Long-term Multi-granularity Deep Framework for Driver Drowsiness Detection

For real-world driver drowsiness detection from videos, the variation of head pose is so large that the existing methods on global face is not capable of extracting effective features, such as looking aside and lowering head. Temporal dependencies with variable length are also rarely considered by the previous approaches, e.g., yawning and speaking. In this paper, we propose a Long-term Multi-granularity Deep Framework to detect driver drowsiness in driving videos containing the frontal faces. The framework includes two key components: (1) Multi-granularity Convolutional Neural Network (MCNN), a novel network utilizes a group of parallel CNN extractors on well-aligned facial patches of different granularities, and extracts facial representations effectively for large variation of head pose, furthermore, it can flexibly fuse both detailed appearance clues of the main parts and local to global spatial constraints; (2) a deep Long Short Term Memory network is applied on facial representations to explore long-term relationships with variable length over sequential frames, which is capable to distinguish the states with temporal dependencies, such as blinking and closing eyes. Our approach achieves 90.05% accuracy and about 37 fps speed on the evaluation set of the public NTHU-DDD dataset, which is the state-of-the-art method on driver drowsiness detection. Moreover, we build a new dataset named FI-DDD, which is of higher precision of drowsy locations in temporal dimension

Breaking through the high redshift bottleneck of Observational Hubble parameter Data: The Sandage-Loeb signal Scheme

We propose a valid scheme to measure the Hubble parameter $H(z)$ at high redshifts by detecting the Sandage-Loeb signal (SL signal) which can be realized by the next generation extremely large telescope. It will largely extend the current observational Hubble parameter data (OHD) towards the redshift region of $z \in [2.0,5.0]$, the so-called "redshift desert", where other dark energy probes are hard to provide useful information of the cosmic expansion. Quantifying the ability of this future measurement by simulating observational data for a CODEX (COsmic Dynamics and EXo-earth experiment)-like survey and constraining various cosmological models, we find that the SL signal scheme brings the redshift upper-limit of OHD from $z_\mathrm{max}=2.3$ to $z_\mathrm{max}\simeq 5.0$, provides more accurate constraints on different dark energy models, and greatly changes the degeneracy direction of the parameters. For the $\Lambda$CDM case, the accuracy of $\Omega_m$ is improved by $58\%$ and the degeneracy between $\Omega_m$ and $\Omega_ {\Lambda}$ is rotated to the vertical direction of $\Omega_k = 0$ line strongly; for the $w$CDM case, the accuracy of $w$ is improved by $15\%$. The Fisher matrix forecast on different time-dependent $w(z)$ is also performed.Comment: accepted for publication in JCA